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Bounds on Malapportionment

Author

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  • Laszlo A. Koczy

    (Game Theory Research Group Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Keleti Faculty of Business and Management, Óbuda University, Budapest)

  • Balazs Sziklai

    (Game Theory Research Group Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Corvinus University of Budapest Department of Operations Research and Actuarial Sciences)

Abstract

Uniformly sized constituencies give voters similar influence on election outcomes. When constituencies are set up, seats are allocated to the administrative units, such as states or counties, using apportionment methods. According to the impossibility result of Balinski and Young, none of the methods satisfying basic monotonicity properties assign a rounded proportional number of seats (the Hare-quota). We study the malapportionment of constituencies and provide a simple bound as a function of the house size for an important class of divisor methods, a popular, monotonic family of techniques.

Suggested Citation

  • Laszlo A. Koczy & Balazs Sziklai, 2018. "Bounds on Malapportionment," CERS-IE WORKING PAPERS 1801, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1801
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    References listed on IDEAS

    as
    1. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.
    2. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," CERS-IE WORKING PAPERS 1716, Institute of Economics, Centre for Economic and Regional Studies.
    3. Biró, Péter & Kóczy, László Á. & Sziklai, Balázs, 2015. "Fair apportionment in the view of the Venice Commission’s recommendation," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 32-41.
    4. Schubert, Glendon & Press, Charles, 1964. "Measuring Malapportionment," American Political Science Review, Cambridge University Press, vol. 58(2), pages 302-327, June.
    5. Oscar R. Burt & Curtis C. Harris, 1963. "Letter to the Editor---Apportionment of the U.S. House of Representatives: A Minimum Range, Integer Solution, Allocation Problem," Operations Research, INFORMS, vol. 11(4), pages 648-652, August.
    6. Samuels, David & Snyder, Richard, 2001. "The Value of a Vote: Malapportionment in Comparative Perspective," British Journal of Political Science, Cambridge University Press, vol. 31(4), pages 651-671, October.
    7. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
    8. E. J. Gilbert & J. A. Schatz, 1964. "Letter to the Editor—An Ill-Conceived Proposal for Apportionment of the U.S. House of Representatives," Operations Research, INFORMS, vol. 12(5), pages 768-773, October.
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    Citations

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    Cited by:

    1. Csóka, Péter & Kondor, Gábor, 2019. "Delegációk igazságos kiválasztása társadalmi választások elméletével [Choosing a fair delegation by social choice theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 771-787.

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    More about this item

    Keywords

    apportionment problem; divisor methods; malapportionment; Hare-quota;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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